Combine the lentils and 2 quarts water in a medium stockpot and bring to a boil over high heat. Reduce the heat to low and simmer until the lentils are soft (but not falling apart), about 25 minutes. Drain the lentils and allow to cool.
Add 1/4 cup of the olive oil to a large frying pan and sauté the onions, carrots, celery, garlic, thyme, and salt over medium-high heat, stirring frequently, for about 10 minutes, until the vegetables are tender and just beginning to brown. Add the tomato paste and continue to cook, stirring constantly, for 3 minutes. Add the mushrooms and cook, stirring frequently, for 15 more minutes, or until all the liquid is absorbed. Transfer the mixture to a large bowl and allow to cool to room temperature. When cool, add the lentils to the vegetable mixture.
Add the eggs, Parmesan, bread crumbs, parsley, and walnuts to the cooled vegetable mixture and mix by hand until thoroughly incorporated. Place in the refrigerator for 25 minutes.
Preheat the oven to 400°F.
Drizzle the remaining 2 tablespoons olive oil into a 9x13-inch baking dish and use your hand to evenly coat the entire surface. Set aside.
Roll the mixture into round, gold ball-size meatballs (about 1 1/2 inches), making sure to pack the vegetable mixture firmly. Place the balls in the prepared baking dish, allowing 1/4-inch of space between the balls and place them in even rows vertically and horizontally to form a grid.
Roast for 30 minutes, or until the meatballs are firm and cooked through.
Allow the meatballs to cool for 5 minutes in the baking dish before serving.
Recipe courtesy of The Meatball Shop Cookbook by Daniel Holzman and Michael Chernow with Lauren Deen/Ballantine Books, 2011.